Symbolic regression (SR) searches for analytical expressions representing the relationship between a set of explanatory and response variables. Current SR methods assume a single dataset extracted from a single experiment. Nevertheless, frequently, the researcher is confronted with multiple sets of results obtained from experiments conducted with different setups. Traditional SR methods may fail to find the underlying expression since the parameters of each experiment can be different. In this work we present Multi-View Symbolic Regression (MvSR), which takes into account multiple datasets simultaneously, mimicking experimental environments, and outputs a general parametric solution. This approach fits the evaluated expression to each independent dataset and returns a parametric family of functions f(x; theta) simultaneously capable of accurately fitting all datasets. We demonstrate the effectiveness of MvSR using data generated from known expressions, as well as real-world data from astronomy, chemistry and economy, for which an a priori analytical expression is not available. Results show that MvSR obtains the correct expression more frequently and is robust to hyperparameters change. In real-world data, it is able to grasp the group behavior, recovering known expressions from the literature as well as promising alternatives, thus enabling the use of SR to a large range of experimental scenarios.

翻译：符号回归（SR）旨在寻找表示解释变量与响应变量之间关系的解析表达式。当前的SR方法假设数据来源于单一实验的单个数据集。然而，研究者常常面临来自不同实验设置的多组结果。传统SR方法可能因各实验参数不同而无法发现潜在表达式。本文提出多视图符号回归（MvSR），该方法同时考虑多个数据集以模拟实验环境，并输出通用的参数化解。该框架将评估表达式分别拟合至各独立数据集，并返回一个参数化函数族f(x; θ)，该函数族能同时精确拟合所有数据集。我们通过已知表达式生成的数据以及来自天文学、化学和经济学的真实数据验证了MvSR的有效性，这些真实数据并无先验解析表达式。结果表明，MvSR能更频繁地获得正确表达式，且对超参数变化具有鲁棒性。在真实数据中，该方法能够捕捉群体行为，既复现了文献中的已知表达式，也发现了有潜力的替代形式，从而将SR的应用范围拓展至更广泛的实验场景。